Hello my teacher sent back my assignment and I need help with the revisions:

PT 1.

Teachers message:

#1 - Can you please explain what you mean by Log₂(x)plug₂(18).Also, I'm not sure where K came from.

#2, 3, 4, 8- Please show how you test for extraneous solutions (which you do have here.)

#10, 11, 12 - Be careful with your symbols.* means multiplication.You should have decimals here.

#13 - This is incorrect, but I'm not quite following your work.When there is no base in a log, the base is 10.

#14 - I'm not following your work after 10log(9x10¹⁰).What did you have for log(9x10¹⁰)?

my assignment:

8. log₂(x - 4) + log₂(x) = 5

Log₂[(x-4)x]=5

2⁵=[x(x-4)]

2⁵=x(x-4)

X(x-4)=32

X²-4x-32=0

X²+4x-8x-32=0

X(x+4)-8(x+4)=0

(x-8)(x+4)=0

X=8 and x=-4

10. log₂(x) = 3.87

X=2^3*87=2^(3*87)=14*62

11. log₂(2x) = 5.23

2x=2^(5*23)=37*5

X=37*5/2=18*75

12. ln(3.1x) = 2.31

3*1x=e^2*31=10*07

X=10.07/3*1=3*24

Solve the following problems showing your steps and including the units of measurement.

13. Earthquake intensity is measured by the Richter scale. The formula for the Richter rating of a given quake is given by "R=log[I/I₀]" where I₀is the "threshold quake", or movement that can barely be detected, and the intensity I is given in terms of multiples of the threshold intensity.

An earthquake was reported to have a Richter number of 5.99. How does the intensity of the earthquake approximately compare with the reference intensity?

Richter scale=R=log[I/I₀]

Since R=5*99

5*99=log_e[I/I₀]

I/I₀=e^5*99=399*4I-> I₀=399*4I

I=I₀₌*=(3*99)

The first intensity=I

The end intensity= 399I

The intensity increased to 399 times as the first value.

14. "Loudness" is measured in decibels. The formula for the loudness of a sound is given by "Db = 10log[ I / I₀]" where I₀is the intensity of "threshold sound", or sound that can barely be perceived. How many decibels is a noise with an intensity of I = (9 * 10¹⁰)I₀?

The loudness=10log[I/I₀]

Since I=9x10¹⁰I₀hence the loudness turns into =10log(I₀9x10¹⁰/9xI₀¹⁰)

=10log(9x10¹⁰)=10x9*954=99*54 dB

PT 2.

The other teacher message:

It looks like you misread the exponents on these, but I can't tell when you have exponents and when you don't.

the assignment and my answers:

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